We explore transitions in suspensions of fd virus at a low ionic strength, induced by external electric fields at frequencies where double layers are polarized. On the basis of the different optical morphologies, phase/state diagrams are constructed in the field-amplitude versus frequency plane and the field-amplitude versus concentration plane. Due to interactions between polarized double layers, for low frequencies, various phases and dynamical states are found: a nematic phase, a striped phase and a dynamical state where nematic domains melt and reform. At relatively high frequencies of a few kHz, a uniform homeotropic phase is induced. The various phases and states are characterized by means of polarization microscopy, birefringence, dynamic light scattering and video-correlation spectroscopy. An expression is derived for the attenuation of the electric field due to electrode polarization, which is tested experimentally. This theory is used to correct phase/state diagrams for electrode polarization.